Oscar's back yard is in the shape of a rectangle. It has an area
of 45 square meters. The length of Oscar's yard is 75 meters.
What is the width?

the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are

distinct prime numbers is 1.

To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.

First, let's find the prime factors of the given numbers:

x = a prime number (distinct from y and z)

2y = 2 × y

3y = 3 × y

4z = 2² × z

3z = 3 × z

x² = a prime number squared (distinct from y and z)

5 = a prime number

Next, we can pair up the numbers and find their common factors:

Common factors of x and 2y: 1, 2, y

Common factors of 3y and 4z: 1, 2, 3, y, z, 6

Common factors of x² and 3z: 1, 3, x, z, xz

Common factors of 5 and 2: 1

Finally, we find the highest common factor of all the resulting common factors:

The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.

Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.

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Answer: When an epitaxial layer is grown on a substrate, the lattice constant of the epitaxial layer may differ from that of the substrate, leading to strain in the layer. In the case of a simple cubic lattice, the lattice constant can be defined as the distance between two adjacent atoms along any lattice vector.

The lattice mismatch between the substrate and the epitaxial layer can be quantified by the lattice mismatch parameter, δ, which is defined as:

δ = (a2 - a1) / a1

where a1 is the lattice constant of the substrate and a2 is the lattice constant of the epitaxial layer. If δ is positive, the epitaxial layer is under compressive strain, while if δ is negative, the epitaxial layer is under tensile strain.

The strain in the epitaxial layer can also be quantified by the strain parameter, ε, which is defined as:

ε = (a2 - a1) / a2

In the case of a simple cubic lattice, the strain parameter is equal to the lattice mismatch parameter, i.e., ε = δ.

When an epitaxial layer is grown, it may undergo island formation due to the strain induced by the lattice mismatch with the substrate. The thickness of the epitaxial layer at which island formation occurs can be estimated using the critical thickness, t_c, which is given by:

t_c = (h_bar^2 * δ^2) / (2 * E * γ)

where h_bar is the reduced Planck constant, E is the elastic modulus of the epitaxial layer, and γ is the surface energy of the epitaxial layer.

If the thickness of the epitaxial layer is less than the critical thickness, the epitaxial layer remains continuous and undergoes strain relaxation. If the thickness of the epitaxial layer is greater than the critical thickness, the epitaxial layer undergoes island formation.

In summary, the growth of an epitaxial layer on a substrate with a different lattice constant can lead to strain in the layer, which can result in island formation at a critical thickness. The critical thickness can be estimated using the lattice mismatch parameter, elastic modulus, and surface energy of the epitaxial layer.

Epitaxial growth refers to the process of depositing a thin layer of material on a substrate such that the crystal structure of the layer mimics that of the substrate. In this case, we are considering the growth of an epitaxial layer of thickness t2 with a relaxed (unstrained) lattice constant a2 on a substrate with a relaxed lattice constant a1.

Assuming a simple cubic lattice for simplicity, we can use the equation for lattice mismatch to calculate the strain between the layer and substrate:

ε = (a2 - a1) / a1

If the lattice constants are matched, ε = 0 and there is no strain. However, if there is a mismatch, there will be strain in the layer. In the case of a relaxed layer, we assume that the strain has been relieved and the layer has reached equilibrium with the substrate.

The thickness of the layer, t2, can affect the strain in the layer. Generally, thinner layers will have less strain because they are more able to conform to the lattice of the substrate. Thicker layers may have more strain, which can lead to defects in the layer.

Overall, the thickness of the epitaxial layer can affect the strain in the layer and should be carefully controlled to minimize defects.

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Using fraction formula ,

The flour used by ramil and Carly for making bread is 33/40lb

Fraction: fraction is a number represented as a quotient, in which a numerator is divided by a denominator.

We have given that,

Ramil and Carly used 1/2 lb flour to make the bread.

They used 1/8lb less flour to make bread than to make cookies.

So, they used flour to make the cookies = 1/2+1/8

= 5/8lb

Therefore they used 5/8lb flour to make the cookies.

they used 1/5 lb more breads to make cookies than to make brownies. Mathematically, they used cookies for making the brownies is

= 1/5 + 5/8

=(8 + 25)/40 = 33/40lb

Therefore , they used 33/40lb flour to make the brownies.

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Complete question:

Ramil amd carly decided to make more baked goods for the bake sale. They used 1/8 lb less flour to make bread than to make cookies. She used 1/5 lb more to make cookies than to make brownies. If she used 1/2 lb of flour to make the bread, how much flour did she use to make the brownies

The transformation applied to the letter R is given as follows:

B. Translation.

Examples of transformations are given as follows:

In the context of this problem, we have that the letter underwent a lateral movement, without changing the orientation, hence it underwent only a translation.

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The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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Answer:

#1. is slope

#2. Is 300

#3. ///

Step-by-step explanation:

#1. Slope is represented by m in slope intercept form.

#2. The money is increasing by $300 every week, resulting in a slope of 300/1

#3 ///

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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11.55 years are required to reach $7900 from $5000 at an interest of 4%

Compound interest, also known as interest on principal amount, is the practice of adding interest to the principal amount of a loan or deposit.

Given p= $5000

rate of interest = 4% and compounded semi-annually

n=2 (for compounded semi annually)

let the time duration be t

and given Amount = $7900

we know formula of compund interest:

A= \(P(1+\frac{r}{100n})^n^t\)

=> 7900 = 5000\((1+\frac{0.04}{2} )^2^t\)

=> 7900 = 5000 \((1.02)^2^t\)

=> \((1.02)^2^t\) = 1.58

taking ln on both side

2t ln(1.02) = ln(1.58)

2t = ln(1.58)/(ln(1.02)

=> 2t= 23.099

=> t = 23.099/2

=> t = 11.55 years

so the time duration is 11.55 years

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The best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.

To determine the best approximation for the area of this circle, we need to use the formula for the area of a circle, which is given by A = πr².

Here, we are given the value of π to be approximately equal to 3.14.

Now, we need to determine the radius of the circle.

From the diagram, we can see that the diameter of the circle is 8 meters.

Therefore, the radius is half of this, which is 4 meters.

Substituting the values of π and r into the formula, we get: A = πr²= 3.14 × 4²= 3.14 × 16= 50.24 (to two decimal places)

Therefore, the best approximation for the area of this circle is approximately 50.2 m².Option (c) is the correct answer.

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Answer:

A

Step-by-step explanation:

beacuse when you subsiture the numberz you exactly get letters A answer which completers the function of the table by subsituting the numbers in tge equation

To find the area under the standard normal curve, follow the following steps: Step 1: Draw the Standard Normal Curve. The standard normal curve is a symmetrical bell-shaped curve. The horizontal axis represents the z-values, which represent the standard deviations from the mean of the curve. The vertical axis represents the probability density, which indicates the likelihood of each z-value occurring. Step 2: Identify the Area of Interest. Under the standard normal curve, the area of interest is the shaded region that represents the probability of an event occurring. The event can be a range of z-values or a specific z-value. The area under the curve represents the probability of the event occurring. Step 3: Use the Standard Normal Table.

The standard normal table is a table of values that corresponds to the area under the curve for different z-values. The table provides the area to the left of a given z-value. To find the area between two z-values, subtract the area to the left of the smaller z-value from the area to the left of the larger z-value. The area to the right of a z-value can be found by subtracting the area to the left of the z-value from 1. To find the area for a specific z-value, use the standard normal table to find the area to the left of the z-value. Step 4: Calculate the Area.

Under the standard normal curve, the area is measured in units of standard deviation. The area between two z-values or to the right of a z-value can be calculated by multiplying the area from the standard normal table by the standard deviation of the curve. For example, if the area to the left of a z-value is 0.35 and the standard deviation of the curve is 2, then the area between the mean and the z-value is 0.35 x 2 = 0.70 square units. The area to the right of the z-value is 1 - 0.35 = 0.65, so the area beyond the z-value is 0.65 x 2 = 1.30 square units.

In summary, to find the area under the standard normal curve, draw the curve, identify the area of interest, use the standard normal table to find the area to the left of the z-value, and calculate the area in units of standard deviation. This calculation helps to interpret the probability of an event occurring in a given population. In about 200 words, this is how to find the area under the standard normal curve.

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The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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Answer:

It is in standard form, unless you say you want to write it in whole number form, move it six points to the left

Step-by-step explanation:

The prefix for one million in the metric system is "mega-". The prefix "mega-" is derived from the Greek word "megas" which means large. It is used to denote a factor of one million, or 10^6.

To illustrate, let's consider the metric unit of length, the meter. If we add the prefix "mega-" to meter, we get the unit "megameter" (Mm). One megameter is equal to one million meters.

Similarly, if we consider the metric unit of grams, the prefix "mega-" can be added to form the unit "megagram" (Mg). One megagram is equal to one million grams.

In summary, the prefix for one million in the metric system is "mega-". It is used to denote a factor of 10^6 and can be added to various metric units to represent quantities of one million, such as megameter (Mm) or megagram (Mg).

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Answer:

x_>0,_>3000

Step-by-step explanation:

I saw the answer key :)

The domain of a function is the set of input values the function can take.

The reasonable domain of the function is [0,16]

From the question, we understand that x represents the number of years after 2000 until 2016.

Hence, the reasonable domain of the function is [0,16]

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Answer:

3

Step-by-step explanation:

The answer is 3 because first you add -2 + 1 which is -1 then you multiply -3 by -1 and you get 3

Answer:

$1680

Step-by-step explanation:

Principal loan amount x Interest rate x Time

= 12000 × 14% × 1

=12000 × 14/100 × 1

=168000/100 × 1

=1680

Answer:

i hope this helps!

credit: sayaksjunkyard2018

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Step-by-step explanation:

P = $ 12000

r = 14%

t = 1 (for first year)

I = (P X r X t)/100

∴ I = (12000 X 14 X 1)/100

   = 120 X 14

   = $ 1680   <---------- (Interest on loan at the end of first year)

∴ Total amount owing at the end of first year = (P + I)

                                                                          = (12000 + 1680)

                                                                          =  $ 13680

Repayment = $ 7800

Amount still outstanding (at the start of second year) = 13680 - 7800

                                                                                       =  $ 5880

Interest on the outstanding amount at the end of second year,

P (new) = $ 5880

r (same) = 14%

t = 1 (for the current second year)

∴ I = (P X r X t)/100

   = (5880 X 14 X 1)/100

   = 82320 / 100

   = $ 823.2   <-------------------------- (Interest on outstanding amount at the end of second year)

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

Answer:

the formula is :

area = 1/2(b1 + b2) x h

in this case it's :

area = 1/2(3 + b2)x 4

You will need the length of the lower base to solve it.

Step-by-step explanation:

The equation which models the relationship expressed in slope intercept form ls y = 45x

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a  linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

Expressing the equation in the form :

y = bx + c

Slope, b = (900 - 225) / (20 - 5) = 45

Using any (x, y) points on the table given to find the value of c :

225 = 45(5) + c

225 = 225 + c

c = 0

Hence, the equation which models the relationship is y = 45x

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Answer:

the answer is c, (-10,4) and the radius is 10

Step-by-step explanation:

Hope this helps!❆

Answer:

√52 units

Step-by-step explanation:

Here we want to find the distance between two points;

O(0,0) and A (4,6)

We can use the distance formula to find this;

D = √(x2-x1)^2 + (y2-y1)^2

D = √(4-0)^2 + (6-0)^2

D = √(16 + 36)

D = √52

So the distance between the two points is √52 units

Answer:

x=2

Step-by-step explanation:

4*2-3/3

then u have to trust me

Yes, the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean.

To determine whether the confidence interval contains the true mean of 33, we need to calculate the margin of error for the confidence interval. The margin of error is a measure of the precision of the estimate, and it is calculated using the sample size, the standard deviation of the population, and the desired level of confidence.

For a 95% confidence interval, the margin of error can be calculated using the following formula:

The margin of error = 1.96 * (standard deviation / √sample size)

Plugging in the values, we get:

Margin of error = 1.96 * (14 / √42)

Performing the calculation, we find that the margin of error is 3.39. This means that the sample mean of 31 is likely to be within 3.39 units of the true mean, with a confidence level of 95%.

Since the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean. This means that our estimate of the population mean, based on the sample size 42, is likely to be accurate.

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Answer:

The number of times a variable appears in a date set is called a constant.

100 grams i think? not entirely sure

Answer: 600 grams

Step-by-step explanation:

Mass does not change with gravity. Weight changes with gravity

Answer:

37. 0 triangles

38. 1 triangle

39. Yes

40. 13 or greater

Step-by-step explanation:

According to the triangle inequality theorem, the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side, so since 5 + 8 = 13, the third side must not be 13 or greater.